Question: $ B = \left[\begin{array}{rr}-2 & 0 \\ -1 & 3 \\ 4 & 1\end{array}\right]$ $ F = \left[\begin{array}{rrr}-2 & 4 & 3 \\ -2 & 2 & 3 \\ 4 & 0 & 2\end{array}\right]$ Is $ B- F$ defined?
Answer: In order for subtraction of two matrices to be defined, the matrices must have the same dimensions. If $ B$ is of dimension $( m \times  n)$ and $ F$ is of dimension $( p \times  q)$ , then for their difference to be defined: 1. $ m$ (number of rows in $ B$ ) must equal $ p$ (number of rows in $ F$ ) and 2. $ n$ (number of columns in $ B$ ) must equal $ q$ (number of columns in $ F$ Do $ B$ and $ F$ have the same number of rows? Yes Yes No Yes Do $ B$ and $ F$ have the same number of columns? No Yes No No Since $ B$ has different dimensions $(3\times2)$ from $ F$ $(3\times3)$, $ B- F$ is not defined.